The discontinuous Galerkin approximation of the grad-div and curl-curl operators in first-order form is involution-preserving and spectrally correct - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles SIAM Journal on Numerical Analysis Year : 2023

The discontinuous Galerkin approximation of the grad-div and curl-curl operators in first-order form is involution-preserving and spectrally correct

Abstract

The discontinuous Galerkin approximation of the grad-div and curl-curl problems formulated in conservative first-order form is investigated. It is shown that the approximation is spectrally correct, thereby confirming numerical observations made by various authors in the literature. This result hinges on the existence of discrete involutions which are formulated as discrete orthogonality properties. The involutions are crucial to establish discrete versions of weak Poincaré-Steklov inequalities that hold at the continuous level.
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Dates and versions

hal-04003475 , version 1 (24-02-2023)
hal-04003475 , version 2 (29-06-2023)

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Alexandre Ern, Jean-Luc Guermond. The discontinuous Galerkin approximation of the grad-div and curl-curl operators in first-order form is involution-preserving and spectrally correct. SIAM Journal on Numerical Analysis, 2023, 61 (6), pp.2940-2966. ⟨10.1137/23M1555235⟩. ⟨hal-04003475v2⟩
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